{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第一讲：方程组的几何解释\n",
    "\n",
    "我们从求解线性方程组来开始这门课，从一个普通的例子讲起：方程组有$2$个未知数，一共有$2$个方程，分别来看方程组的“行图像”和“列图像”。\n",
    "\n",
    "有方程组$\\begin{cases}2x&-y&=0\\\\-x&+2y&=3\\end{cases}$，写作矩阵形式有$\\begin{bmatrix}2&-1\\\\-1&2\\end{bmatrix}\\begin{bmatrix}x\\\\y\\end{bmatrix}=\\begin{bmatrix}0\\\\3\\end{bmatrix}$，通常我们把第一个矩阵称为系数矩阵$A$，将第二个矩阵称为向量$x$，将第三个矩阵称为向量$b$，于是线性方程组可以表示为$Ax=b$。\n",
    "\n",
    "我们来看行图像，即直角坐标系中的图像："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "#解决中文显示问题\n",
    "plt.rcParams['font.sans-serif'] = ['KaiTi'] # 指定默认字体\n",
    "plt.rcParams['axes.unicode_minus'] = False # 解决保存图像是负号'-'显示为方块的问题\n",
    "\n",
    "x = np.arange(-5, 5)\n",
    "y = 2 * x\n",
    "\n",
    "y1 = (x + 3) / 2\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.title('基础线性代数')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.axhline(y=0, c='black')\n",
    "plt.axvline(x=0, c='black')\n",
    "plt.grid() \n",
    "plt.plot(x, y)\n",
    "plt.plot(x, y1)\n",
    "\n",
    "plt.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "plt.close(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上图是我们都很熟悉的直角坐标系中两直线相交的情况，接下来我们按列观察方程组$x\\begin{bmatrix}2\\\\-1\\end{bmatrix}+y\\begin{bmatrix}-1\\\\2\\end{bmatrix}=\\begin{bmatrix}0\\\\3\\end{bmatrix}$（我们把第一个向量称作$col_1$，第二个向量称作$col_2$，以表示第一列向量和第二列向量），要使得式子成立，需要第一个向量加上两倍的第二个向量，即$1\\begin{bmatrix}2\\\\-1\\end{bmatrix}+2\\begin{bmatrix}-1\\\\2\\end{bmatrix}=\\begin{bmatrix}0\\\\3\\end{bmatrix}$。\n",
    "\n",
    "现在来看列图像，在二维平面上画出上面的列向量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from functools import partial\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.title('按列观察方程组')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.axhline(y=0, c='black')\n",
    "plt.axvline(x=0, c='black')\n",
    "plt.grid() \n",
    "ax = plt.gca()\n",
    "ax.set_xlim(-2.5, 2.5)\n",
    "ax.set_ylim(-3, 4)\n",
    "\n",
    "\n",
    "x = np.arange(-5, 5)\n",
    "y = - x / 2\n",
    "y_ = x\n",
    "y_1 = (x + 3) / 2\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.plot(x, y)\n",
    "plt.plot(x, y_)\n",
    "\n",
    "plt.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "plt.close(fig)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from functools import partial\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.title('按列观察方程组')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.axhline(y=0, c='black')\n",
    "plt.axvline(x=0, c='black')\n",
    "plt.grid() \n",
    "ax = plt.gca()\n",
    "ax.set_xlim(-2.5, 2.5)\n",
    "ax.set_ylim(-3, 4)\n",
    "\n",
    "arrow_vector = partial(plt.arrow, width=0.01, head_width=0.1, head_length=0.2, length_includes_head=True)\n",
    "\n",
    "arrow_vector(0, 0, 2, -1, color='g')\n",
    "arrow_vector(0, 0, -1, 2, color='c')\n",
    "arrow_vector(2, -1, -2, 4, color='b')\n",
    "arrow_vector(0, 0, 0, 3, width=0.05, color='r')\n",
    "\n",
    "plt.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "plt.close(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如图，绿向量$col_1$与蓝向量（两倍的蓝绿向量$col_2$）合成红向量$b$。\n",
    "\n",
    "接着，我们继续观察$x\\begin{bmatrix}2\\\\-1\\end{bmatrix}+y\\begin{bmatrix}-1\\\\2\\end{bmatrix}=\\begin{bmatrix}0\\\\3\\end{bmatrix}$，$col_1,col_2$的某种线性组合得到了向量$b$，那么$col_1,col_2$的所有线性组合能够得到什么结果？它们将铺满整个平面。\n",
    "\n",
    "下面进入三个未知数的方程组：$\\begin{cases}2x&-y&&=0\\\\-x&+2y&-z&=-1\\\\&-3y&+4z&=4\\end{cases}$，写作矩阵形式$A=\\begin{bmatrix}2&-1&0\\\\-1&2&-1\\\\0&-3&4\\end{bmatrix},\\ b=\\begin{bmatrix}0\\\\-1\\\\4\\end{bmatrix}$。\n",
    "\n",
    "在三维直角坐标系中，每一个方程将确定一个平面，而例子中的三个平面会相交于一点，这个点就是方程组的解。\n",
    "\n",
    "同样的，将方程组写成列向量的线性组合，观察列图像：$x\\begin{bmatrix}2\\\\-1\\\\0\\end{bmatrix}+y\\begin{bmatrix}-1\\\\2\\\\-3\\end{bmatrix}+z\\begin{bmatrix}0\\\\-1\\\\4\\end{bmatrix}=\\begin{bmatrix}0\\\\-1\\\\4\\end{bmatrix}$。易知教授特意安排的例子中最后一个列向量恰巧等于等式右边的$b$向量，所以我们需要的线性组合为$x=0,y=0,z=1$。假设我们令$b=\\begin{bmatrix}1\\\\1\\\\-3\\end{bmatrix}$，则需要的线性组合为$x=1,y=1,z=0$。\n",
    "\n",
    "我们并不能总是这么轻易的求出正确的线性组合，所以下一讲将介绍消元法——一种线性方程组的系统性解法。\n",
    "\n",
    "现在，我们需要考虑，对于任意的$b$，是否都能求解$Ax=b$？用列向量线性组合的观点阐述就是，列向量的线性组合能否覆盖整个三维向量空间？对上面这个例子，答案是肯定的，这个例子中的$A$是我们喜欢的矩阵类型，但是对另一些矩阵，答案是否定的。那么在什么情况下，三个向量的线性组合得不到$b$？\n",
    "\n",
    "——如果三个向量在同一个平面上，问题就出现了——那么他们的线性组合也一定都在这个平面上。举个例子，比如$col_3=col_1+col_2$，那么不管怎么组合，这三个向量的结果都逃不出这个平面，因此当$b$在平面内，方程组有解，而当$b$不在平面内，这三个列向量就无法构造出$b$。在后面的课程中，我们会了解到这种情形称为**奇异**、**矩阵不可逆**。\n",
    "\n",
    "下面我们推广到九维空间，每个方程有九个未知数，共九个方程，此时已经无法从坐标图像中描述问题了，但是我们依然可以从求九维列向量线性组合的角度解决问题，仍然是上面的问题，是否总能得到$b$？当然这仍取决于这九个向量，如果我们取一些并不相互独立的向量，则答案是否定的，比如取了九列但其实只相当于八列，有一列毫无贡献（这一列是前面列的某种线性组合），则会有一部分$b$无法求得。\n",
    "\n",
    "接下来介绍方程的矩阵形式$Ax=b$，这是一种乘法运算，举个例子，取$A=\\begin{bmatrix}2&5\\\\1&3\\end{bmatrix},\\ x=\\begin{bmatrix}1\\\\2\\end{bmatrix}$，来看如何计算矩阵乘以向量：\n",
    "\n",
    "* 我们依然使用列向量线性组合的方式，一次计算一列，$\\begin{bmatrix}2&5\\\\1&3\\end{bmatrix}\\begin{bmatrix}1\\\\2\\end{bmatrix}=1\\begin{bmatrix}2\\\\1\\end{bmatrix}+2\\begin{bmatrix}5\\\\3\\end{bmatrix}=\\begin{bmatrix}12\\\\7\\end{bmatrix}$\n",
    "* 另一种方法，使用向量内积，矩阵第一行向量点乘$x$向量$\\begin{bmatrix}2&5\\end{bmatrix}\\cdot\\begin{bmatrix}1&2\\end{bmatrix}^T=12,\\ \\begin{bmatrix}1&3\\end{bmatrix}\\cdot\\begin{bmatrix}1&2\\end{bmatrix}^T=7$。\n",
    "\n",
    "教授建议使用第一种方法，将$Ax$看做$A$列向量的线性组合。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
     "data": {
      "text/plain": "<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x298037ef148>"
     },
     "metadata": {},
     "output_type": "execute_result",
     "execution_count": 1
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from mpl_toolkits.mplot3d.axes3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "axes3d = Axes3D(fig)\n",
    "\n",
    "# !! 面\n",
    "x = np.linspace(-10, 10 , 100)\n",
    "y = np.linspace(-10 , 10 , 100)\n",
    "z = np.linspace(-10 , 10 , 100)\n",
    "\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "axes3d.plot_surface(X,Y, -X + 2*Y + 1)\n",
    "\n",
    "X, Z = np.meshgrid(x, z)\n",
    "axes3d.plot_surface(X,2 * X, Z)\n",
    "\n",
    "X, Y = np.meshgrid(x, y)\n",
    "axes3d.plot_surface(X,Y, 1 - 3 * Y / 4)"
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